My Haken company is stalling my visa renewal

Hi, I am currently a resident on a 1-year engineer visa. I work as a Haken Shain, with a 3 month rolling contract. So far my contract has been renewed 3 times without fail and I am not worried about not being renewed, but my current contract ends dangerously close (11 days) from my visa expiration date early April.

I was going to submit my visa extension application 2 months before the limit, but I am missing some documents from my employer and they are now telling me they will take care of the visa procedure after my contract is renewed.

Even if my contract renewal happens a little over a month before my visa renewal (1 month before the current contract expiration) I worry this is dangerously short. Additionally, I was hoping to apply for a 5 years work visa but I have no guarantee my employer will ask the same.

Should I insist on applying by myself and ask for the missing documents? Or trust my employer to do the application after my contract is renewed ?

by Plinytheyoung